Man page - gesv_mixed(3)

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Manual

gesv_mixed

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dsgesv (integer n, integer nrhs, double precision, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, doubleprecision, dimension( ldb, * ) b, integer ldb, double precision,dimension( ldx, * ) x, integer ldx, double precision, dimension( n, * )work, real, dimension( * ) swork, integer iter, integer info)
subroutine zcgesv (integer n, integer nrhs, complex*16, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integerldx, complex*16, dimension( n, * ) work, complex, dimension( * ) swork,double precision, dimension( * ) rwork, integer iter, integer info)
Author

NAME

gesv_mixed - gesv: factor and solve, mixed precision

SYNOPSIS

Functions

subroutine dsgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, iter, info)
DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)
subroutine zcgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, rwork, iter, info)
ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Detailed Description

Function Documentation

subroutine dsgesv (integer n, integer nrhs, double precision, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, doubleprecision, dimension( ldb, * ) b, integer ldb, double precision,dimension( ldx, * ) x, integer ldx, double precision, dimension( n, * )work, real, dimension( * ) swork, integer iter, integer info)

DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Purpose:

DSGESV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

DSGESV first attempts to factorize the matrix in SINGLE PRECISION
and use this factorization within an iterative refinement procedure
to produce a solution with DOUBLE PRECISION normwise backward error
quality (see below). If the approach fails the method switches to a
DOUBLE PRECISION factorization and solve.

The iterative refinement is not going to be a winning strategy if
the ratio SINGLE PRECISION performance over DOUBLE PRECISION
performance is too small. A reasonable strategy should take the
number of right-hand sides and the size of the matrix into account.
This might be done with a call to ILAENV in the future. Up to now, we
always try iterative refinement.

The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH(’Epsilon’)
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.

Parameters

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

A

A is DOUBLE PRECISION array,
dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.
On exit, if iterative refinement has been successfully used
(INFO = 0 and ITER >= 0, see description below), then A is
unchanged, if double precision factorization has been used
(INFO = 0 and ITER < 0, see description below), then the
array A contains the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
Corresponds either to the single precision factorization
(if INFO = 0 and ITER >= 0) or the double precision
factorization (if INFO = 0 and ITER < 0).

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X

X is DOUBLE PRECISION array, dimension (LDX,NRHS)
If INFO = 0, the N-by-NRHS solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

WORK

WORK is DOUBLE PRECISION array, dimension (N,NRHS)
This array is used to hold the residual vectors.

SWORK

SWORK is REAL array, dimension (N*(N+NRHS))
This array is used to use the single precision matrix and the
right-hand sides or solutions in single precision.

ITER

ITER is INTEGER
< 0: iterative refinement has failed, double precision
factorization has been performed
-1 : the routine fell back to full precision for
implementation- or machine-specific reasons
-2 : narrowing the precision induced an overflow,
the routine fell back to full precision
-3 : failure of SGETRF
-31: stop the iterative refinement after the 30th
iterations
> 0: iterative refinement has been successfully used.
Returns the number of iterations

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) computed in DOUBLE PRECISION is
exactly zero. The factorization has been completed,
but the factor U is exactly singular, so the solution
could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zcgesv (integer n, integer nrhs, complex*16, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integerldx, complex*16, dimension( n, * ) work, complex, dimension( * ) swork,double precision, dimension( * ) rwork, integer iter, integer info)

ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Purpose:

ZCGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

ZCGESV first attempts to factorize the matrix in COMPLEX and use this
factorization within an iterative refinement procedure to produce a
solution with COMPLEX*16 normwise backward error quality (see below).
If the approach fails the method switches to a COMPLEX*16
factorization and solve.

The iterative refinement is not going to be a winning strategy if
the ratio COMPLEX performance over COMPLEX*16 performance is too
small. A reasonable strategy should take the number of right-hand
sides and the size of the matrix into account. This might be done
with a call to ILAENV in the future. Up to now, we always try
iterative refinement.

The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH(’Epsilon’)
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.

Parameters

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

A

A is COMPLEX*16 array,
dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.
On exit, if iterative refinement has been successfully used
(INFO = 0 and ITER >= 0, see description below), then A is
unchanged, if double precision factorization has been used
(INFO = 0 and ITER < 0, see description below), then the
array A contains the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
Corresponds either to the single precision factorization
(if INFO = 0 and ITER >= 0) or the double precision
factorization (if INFO = 0 and ITER < 0).

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

X

X is COMPLEX*16 array, dimension (LDX,NRHS)
If INFO = 0, the N-by-NRHS solution matrix X.

LDX

LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).

WORK

WORK is COMPLEX*16 array, dimension (N,NRHS)
This array is used to hold the residual vectors.

SWORK

SWORK is COMPLEX array, dimension (N*(N+NRHS))
This array is used to use the single precision matrix and the
right-hand sides or solutions in single precision.

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

ITER

ITER is INTEGER
< 0: iterative refinement has failed, COMPLEX*16
factorization has been performed
-1 : the routine fell back to full precision for
implementation- or machine-specific reasons
-2 : narrowing the precision induced an overflow,
the routine fell back to full precision
-3 : failure of CGETRF
-31: stop the iterative refinement after the 30th
iterations
> 0: iterative refinement has been successfully used.
Returns the number of iterations

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, U(i,i) computed in COMPLEX*16 is exactly
zero. The factorization has been completed, but the
factor U is exactly singular, so the solution
could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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